SOLUTION: ABC Ltd . produces cartridges for the latest printer , and they are sold in
boxes of 8. Unfortunately, 2% of them are faulty. Find the probability that a
given box has at least o
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Question 1120617: ABC Ltd . produces cartridges for the latest printer , and they are sold in
boxes of 8. Unfortunately, 2% of them are faulty. Find the probability that a
given box has at least one faulty cartridge in it.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
probability of failure is .02
probability of no failure is 1 - .02 = .98
the formula to use is p(x) = p^x * q^x * c(n,x)
p is the probability of failure
q is the probability of no failure
x is the number of failures.
n-x is the number of no failures
c(n,x) is the number of ways to get sets of x elements out of sets of n elements without worrying about order within each set.
total probability is always equal to 1.
probability of at least 1 failure is equal to 1 minus probability of no failures.
in your problem.
n = 8
p = .02
q = .98
x = 0 through 8.
p(0) = .02^0 * .98^(8-0) * c(8,0)
this becomes p(0) = 1 * .98^8 * c(8,0) which becomes:
p(0) = 1 * .850763023 * 1 which becomes:
p(0) = 850763023.
probability of at least 1 failure is therefore equal to 1 minus .850763023.
this results in probability of at least 1 failure = .149236977.
all the probabilities of failure are captured in the following excel spreadsheet.
n! = n * (n-1) * (n-2) * (n-3) * ..... * (n-n + 1)
for example, if n = 5, then n! = 5 * 4 * 3 * 2 * 1
n is 5
n-1 is 4
n-2 is 3
n-3 is 2
n-4 is 1
n-4 is the same as n-n+1 = 5-5+1 = 0+1 = 1
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